final final tings

Author: pat-alt

paper/paper.Rmd

@@ -125,10 +125,6 @@ knitr::opts_chunk$set(
 ```{r, child=child_docs}
 ```
 
-# Acknowledgement {-}
-
-Some of the members of TU Delft were partially funded by ICAI AI for Fintech Research, an ING --- TU Delft collaboration. 
-
 # References {.unnumbered}
 
 ::: {#refs}
@@ -140,4 +136,8 @@ Some of the members of TU Delft were partially funded by ICAI AI for Fintech Res
 
 Granular results for all of our experiments can be found in this online companion: [https://www.paltmeyer.com/endogenous-macrodynamics-in-algorithmic-recourse/](https://www.paltmeyer.com/endogenous-macrodynamics-in-algorithmic-recourse/). The Github repository containing all the code used to produce the results in this paper can be found here: [https://github.com/pat-alt/endogenous-macrodynamics-in-algorithmic-recourse](https://github.com/pat-alt/endogenous-macrodynamics-in-algorithmic-recourse).
 
+# Acknowledgements {-}
+
+Some of the members of TU Delft were partially funded by ICAI AI for Fintech Research, an ING --- TU Delft collaboration. 
+
 

paper/paper.pdf

@@ -1,3 +1,3 @@
 # Concluding Remarks {#conclusion}
 
-This work has revisited and extended some of the most general and defining concepts underlying the literature on Counterfactual Explanations and, in particular, Algorithmic Recourse. We demonstrate that long-held beliefs as to what defines optimality in AR, may not always be suitable. Specifically, we run experiments that simulate the application of recourse in practice using various state-of-the-art counterfactual generators and find that all of them induce substantial domain and model shifts. We argue that these shifts should be considered as an expected external cost of individual recourse and call for a paradigm shift from individual to collective recourse in these types of situations. By proposing an adapted counterfactual search objective that incorporates this cost, we make that paradigm shift explicit. We show that this modified objective lends itself to mitigation strategies that can be used to effectively decrease the magnitude of induced domain and model shifts. Through our work, we hope to inspire future research on this important topic. To this end we have open-sourced all of our code along with a Julia package: [`AlgorithmicRecourseDynamics.jl`](https://anonymous.4open.science/r/AlgorithmicRecourseDynamics/README.md). Future researchers should find it relatively easy to replicate, modify and extend the simulation experiments presented here and apply to their own custom counterfactual generators. 
+This work has revisited and extended some of the most general and defining concepts underlying the literature on Counterfactual Explanations and, in particular, Algorithmic Recourse. We demonstrate that long-held beliefs as to what defines optimality in AR, may not always be suitable. Specifically, we run experiments that simulate the application of recourse in practice using various state-of-the-art counterfactual generators and find that all of them induce substantial domain and model shifts. We argue that these shifts should be considered as an expected external cost of individual recourse and call for a paradigm shift from individual to collective recourse in these types of situations. By proposing an adapted counterfactual search objective that incorporates this cost, we make that paradigm shift explicit. We show that this modified objective lends itself to mitigation strategies that can be used to effectively decrease the magnitude of induced domain and model shifts. Through our work, we hope to inspire future research on this important topic. To this end we have open-sourced all of our code along with a Julia package: [`AlgorithmicRecourseDynamics.jl`](https://anonymous.4open.science/r/AlgorithmicRecourseDynamics/README.md). Future researchers should find it easy to replicate, modify and extend the simulation experiments presented here and apply them to their own custom counterfactual generators. 

paper/paper.tex

@@ -1,6 +1,6 @@
 # Experiment Setup {#empirical}
 
-This section presents the exact ingredients and parameter choices describing the simulation experiments we ran to produce the findings presented in the next section (\@ref(empirical-2)). For convenience, we use Algorithm \ref{algo-experiment} as a template to guide us through this section. A few high-level details upfront: each experiment is run for a total of $T=50$ rounds, where in each round we provide recourse to five per cent of all individuals in the non-target class, so $B_t=0.05 * N_t^{\mathcal{D}_0}$^[As mentioned in the previous section, we end up providing recourse to a total of $\approx50\%$ by the end of round $T=50$.]. All classifiers and generative models are retrained for 10 epochs in each round $t$ of the experiment. Rather than retraining models from scratch, we initialize all parameters at their previous levels ($t-1$) and compute backpropagate for 10 epochs using the new training data as inputs into the existing model. Evaluation metrics are computed and stored every 10 rounds. To account for noise, each individual experiment is repeated five times.^[In the current implementation, we use the train-test split each time to only account for stochasticity associated with randomly selecting individuals for recourse. An interesting alternative may be to also perform data splitting each time, thereby adding an additional layer of randomness.]
+This section presents the exact ingredients and parameter choices describing the simulation experiments we ran to produce the findings presented in the next section (\@ref(empirical-2)). For convenience, we use Algorithm \ref{algo-experiment} as a template to guide us through this section. A few high-level details upfront: each experiment is run for a total of $T=50$ rounds, where in each round we provide recourse to five per cent of all individuals in the non-target class, so $B_t=0.05 * N_t^{\mathcal{D}_0}$^[As mentioned in the previous section, we end up providing recourse to a total of $\approx50\%$ by the end of round $T=50$.]. All classifiers and generative models are retrained for 10 epochs in each round $t$ of the experiment. Rather than retraining models from scratch, we initialize all parameters at their previous levels ($t-1$) and backpropagate for 10 epochs using the new training data as inputs into the existing model. Evaluation metrics are computed and stored every 10 rounds. To account for noise, each individual experiment is repeated five times.^[In the current implementation, we use the same train-test split each time to only account for stochasticity associated with randomly selecting individuals for recourse. An interesting alternative may be to also perform data splitting each time, thereby adding an additional layer of randomness.]
 
 ## $M$---Classifiers and Generative Models {#empirical-classifiers}
 
@@ -49,21 +49,21 @@ plt = plot(plts..., layout=(1,4), size=(850,200))
 savefig(plt, "paper/www/synthetic_data.png")
 ```
 
-We use four synthetic binary classification datasets consisting of 1000 samples each: **Overlapping**, **Linearly Separable**, **Circles** and **Moons** (\@ref(fig:synthetic-data)).
+We use four synthetic binary classification datasets consisting of 1000 samples each: **Overlapping**, **Linearly Separable**, **Circles** and **Moons** (Figure \@ref(fig:synthetic-data)).
 
 ```{r synthetic-data, fig.cap="Synthetic classification datasets used in our experiments. Samples from the negative class ($y=0$) are marked in blue while samples of the positive class ($y=1$) are marked in orange."}
 knitr::include_graphics("www/synthetic_data.png")
 ```
 
-Ex-ante we expect to see that by construction, Wachter will create a new cluster of counterfactual instances in the proximity of the initial decision boundary as we saw in Figure \@ref(fig:poc). Thus, the choice of a black-box model may have an impact on the paths of the recourse. For generators that use latent space search (REVISE @joshi2019realistic, CLUE @antoran2020getting) or rely on (and have access to) probabilistic models (CLUE @antoran2020getting, Greedy @schut2021generating) we expect that counterfactuals will end up in regions of the target domain that are densely populated by training samples. Of course, this expectation hinges on how effective said probabilistic models are at capturing predictive uncertainty. Finally, we expect to see the counterfactuals generated by DiCE to be uniformly spread around the feature space inside the target class^[As we mentioned earlier, the diversity constraint used by DiCE is only effective when at least two counterfactuals are being generated. We have therefore decided to always generate 5 counterfactuals for each generator and randomly pick one of them.]. In summary, we expect that the endogenous shifts induced by Wachter outsize those of all other generators since Wachter is not explicitly concerned with generating what we have defined as meaningful counterfactuals. 
+Ex-ante we expect to see that by construction, Wachter will create a new cluster of counterfactual instances in the proximity of the initial decision boundary as we saw in Figure \@ref(fig:poc). Thus, the choice of a black-box model may have an impact on the counterfactual paths. For generators that use latent space search (REVISE @joshi2019realistic, CLUE @antoran2020getting) or rely on (and have access to) probabilistic models (CLUE @antoran2020getting, Greedy @schut2021generating) we expect that counterfactuals will end up in regions of the target domain that are densely populated by training samples. Of course, this expectation hinges on how effective said probabilistic models are at capturing predictive uncertainty. Finally, we expect to see the counterfactuals generated by DiCE to be diversely spread around the feature space inside the target class^[As we mentioned earlier, the diversity constraint used by DiCE is only effective when at least two counterfactuals are being generated. We have therefore decided to always generate 5 counterfactuals for each generator and randomly pick one of them.]. In summary, we expect that the endogenous shifts induced by Wachter outsize those of all other generators since Wachter is not explicitly concerned with generating what we have defined as meaningful counterfactuals. 
 
 ### Real-world data
 
-We use three different real-world datasets from the Finance and Economics domain, all of which are tabular and can be used for binary classification. Firstly, we use the **Give Me Some Credit** dataset which was open-sourced on Kaggle for the task to predict whether a borrower is likely to experience financial difficulties in the next two years [@kaggle2011give], originally consisting of 250,000 instances with 11 numerical attributes. Secondly, we use the **UCI defaultCredit** dataset [@yeh2009comparisons], a benchmark dataset that can be used to train binary classifiers to predict the binary outcome variable of whether credit card clients default on their payment. In its raw form, it consists of 23 explanatory variables: 4 categorical features relating to demographic attributes^[These have been omitted from the analysis. See Section \@ref(limit-data) for details.] and 19 continuous features largely relating to individuals' payment histories and amount of credit outstanding. Both datasets have been used in the literature on AR before (see for example @pawelczyk2021carla, @joshi2019realistic and @ustun2019actionable), presumably because they constitute real-world classification tasks involving individuals that compete for access to credit. 
+We use three different real-world datasets from the Finance and Economics domain, all of which are tabular and can be used for binary classification. Firstly, we use the **Give Me Some Credit** dataset which was open-sourced on Kaggle for the task to predict whether a borrower is likely to experience financial difficulties in the next two years [@kaggle2011give], originally consisting of 250,000 instances with 11 numerical attributes. Secondly, we use the **UCI defaultCredit** dataset [@yeh2009comparisons], a benchmark dataset that can be used to train binary classifiers to predict the binary outcome variable of whether credit card clients default on their payment. In its raw form, it consists of 23 explanatory variables: 4 categorical features relating to demographic attributes and 19 continuous features largely relating to individuals' payment histories and amount of credit outstanding. Both datasets have been used in the literature on AR before (see for example @pawelczyk2021carla, @joshi2019realistic and @ustun2019actionable), presumably because they constitute real-world classification tasks involving individuals that compete for access to credit. 
 
-As a third dataset, we include the **California Housing** dataset derived from the 1990 U.S. census and sourced through scikit-learn [@pedregosa2011scikitlearn, @pace1997sparse]. It consists of 8 continuous features that can be used to predict the median house price for California districts. The continuous outcome variable is binarized as $\tilde{y}=\mathbb{I}_{y>\text{median}(Y)}$ indicating whether or not the median house price of a given district is above or below the median of all districts. While we have not seen this dataset used in the previous literature on AR, others have used the Boston Housing dataset in a similar fashion @schut2021generating. While we initially also conducted experiments on that dataset, we eventually discarded this dataset due to surrounding ethical concerns [@carlisle2019racist].
+As a third dataset, we include the **California Housing** dataset derived from the 1990 U.S. census and sourced through scikit-learn [@pedregosa2011scikitlearn, @pace1997sparse]. It consists of 8 continuous features that can be used to predict the median house price for California districts. The continuous outcome variable is binarized as $\tilde{y}=\mathbb{I}_{y>\text{median}(Y)}$ indicating whether or not the median house price of a given district is above the median of all districts. While we have not seen this dataset used in the previous literature on AR, others have used the Boston Housing dataset in a similar fashion @schut2021generating. We initially also conducted experiments on that dataset, but eventually discarded it due to surrounding ethical concerns [@carlisle2019racist].
 
-Since the simulations involve generating counterfactuals for a significant proportion of the entire sample of individuals, we have randomly undersampled each dataset to yield balanced subsamples consisting of 5,000 individuals each. We have also standardized all explanatory features since our chosen classifiers are sensitive to scale.
+Since the simulations involve generating counterfactuals for a significant proportion of the entire sample of individuals, we have randomly undersampled each dataset to yield balanced subsamples consisting of 5,000 individuals each. We have also standardized all continuous explanatory features since our chosen classifiers are sensitive to scale.
 
 ## $G$---Generators